INFLUENCE OF CERTAIN ELEMENTS ON STEEL. 369 —Several years ago I made investigations by the method of least squares into the influence of the metalloids on open-heaxth steel, and the former editions of this book contained details of the calculations. The following values were found: Acid steel. Basic steel. Ib. per sq. in. Ib. per sq. in. Carbon ......... , ........ 1210 950 Phosphorus ............. 890 1050 Manganese ............ . 85 The base was 38,600 pounds for pure iron for acid steel, and 37,430 pounds for basic metal. These formulae have been used at the works of The Pennsylvania Steel Company for ten yeais, and it is unusual to have a difference of more than 2500 pounds per square inch between the calculated strength and the strength as actually found from the specimen rolled from a test ingot. The values have also been used commercially by other large steel works. In making calculations by least squares, no assumptions are ma-de and no preconceived theory can influence the work. The investigation resolves itself into the solution of certain mathematical equations, with only one possible answer. Notwithstanding this fact, the method has given unsatisfactory results in the hands of other investigators, probably because the number of observations was too limited and the errors too great. In the present case, the general correctness of the results proves that the method is applicable. SBC. XVIIm.—The value of carbon, manganese, phosphorus and iron in open-hearth steel as found ~by plotting.—In a paper read before the New York meeting of the Iron and Steel Institute of Great Britain in October, 1904, I gave the details of an investigation of nearly seven hundred acid heats and eleven hundred basic heats of open-heaxth steel. A complete analysis was made of each heat, the carbon, being determined by combustion. The heats were combined into groups, one group being composed of heats showing carbon from 0.075 to 0.125 per cent.; another with carbon from 0.125 to 0.175 per cent.; and so on, making a division for each additional 0.05 per cent, of carbon. Table XVII-KT gives the list of groups thus formed.